Hide/remove lines in a face
You can hide edges using Bmesh, and it won't hide the faces they're attached to. Users of Sketchup might find this handy but it isn't something you'll find very much use for as your proficiency with Blender increases. But the option is there if you need it.

To run this script you would first select the edges you want to hide, then open the TextEditor window, paste this code into it and press Run.

This example assumes we have a mesh object in Edit Mode, and you have a few edges selected.

import bpy
import bmesh

# Get the active mesh
obj = bpy.context.edit_object
me = obj.data


# Get a BMesh representation
bm = bmesh.from_edit_mesh(me)

bm.faces.active = None

# Modify the BMesh, can do anything here...
for e in bm.edges:
    if e.select:
        e.hide = True


# Show the updates in the viewport
# and recalculate n-gon tessellation.
bmesh.update_edit_mesh(me, True)


to unhide the edges you press Alt+H, while in Edit Mode